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Resources in Understanding Electromagnetism: Building a Conceptual Bridge for Physics Learners and Teachers Carolann Koleci Assistant Professor of Physics Worcester Polytechnic Institute Department of Physics [email protected] edu Friday, May 2, 2008 University at Albany, SUNY

PRELUDE Ask yourself a question Is it what, where, or why? Solving problems requires inquiry So why not give it a try. 2 Worcester Polytechnic Institute

Why is Physics Perceived as Difficult? 3 Fox Trot Cartoon Strip, by: Bill Amend Worcester Polytechnic Institute

HERE’S WHAT REALLY HAPPENED… 4 Worcester Polytechnic Institute

Never Underestimate Creativity lim [ 1/(t – 8) ] = ∞ t→ 8 Now what do you get for: lim [1/(t – 4) ] = t→ 4 5 Worcester Polytechnic Institute

ORGANIZATION • • • Theory/Statement of the Problem Learning Resources in EM Assessment Tools Pilot Study at WPI (Spring 2006) Current Results (some excerpts) Future Directions 6 Worcester Polytechnic Institute

ACKNOWLEDGMENT • Special thanks to Prof. John Belcher, Prof. Sen-Ben Liao, Prof. Peter Dourmashkin, Prof. Sahana Murthy, and the MIT Visualizations Team for their inspiration, collaboration, and support. • We kindly acknowledge support from the Davis Foundation and the NSF. • Thank you to UAlbany (Department of Physics) for the opportunity to share our work. 7 Worcester Polytechnic Institute

STATEMENT OF THE PROBLEM • “I read the book, take notes on the chapter, attend all lectures and recitations, do all of the sample problems from the book, and get ‘good’ grades on my homework, yet I still cannot do well on the exams. ”— anonymous introductory physics student 8 Worcester Polytechnic Institute

EM Road Blocks (excerpts) • Electricity flows like water in a pipe to the receiver. Only needs one wire. • Electrons flow at the speed of light. • Electric companies supply electrons to your house. • Magnets only attract to iron. • Only magnets have magnetic fields. Worcester Polytechnic Institute 9

More Impediments • The Three Principles of EM: V = IR, I = V/R, R = V/I • Coulomb Syndrome • Students accept the existence of a cause only when they can imagine an effect (i. e. to calculate E, only need q(enc) ) • When the RHR becomes the LHR 10 Worcester Polytechnic Institute

Learning Resources in EM • Physlets; Belloni & Christian; Davidson College: http: //webphysics. davidson. edu/cise_qm/ • PHysics Education Technology Project (PHET); University of Colorado (Boulder): http: //www. colorado. edu/physics/Educatio n. Issues/research_projects. htm • Technology Enabled Active Learning (TEAL); MIT: http: //web. mit. edu/8. 02 t/www/802 TEAL 3 D/ visualizations/electrostatics/index. htm 11 Worcester Polytechnic Institute

ON CREATING EXAMS… What it is that a test item measures (that is, its content validity) depends not on what adult experts or critics think it measures nor on what item statistics suggest about the item but rather on how individual testtakers perceive and react to the test or item. . To delve into what it is that a test or test item measures for particular testtakers requires some kind of observation or communication with them on an individual basis (Haney & Scott). 12 Worcester Polytechnic Institute

ON CREATING EXAMS… Likewise, students' classroom experiences play into their perceptions and response to the fairness of testing. Reporting on her interviews with students, Thorkildsen (1999) found that their judgment of how much testing is fair had to do, in part, with the curriculum and instruction they experienced on a day-today basis. Consequently, those taking a test that differs radically in mode or content from their classroom learning may respond negatively to the test itself, especially if the test does not allow them to demonstrate what 13 they know how to do. Worcester Polytechnic Institute

LEARNING AND TRANSFER “Learning often cannot be translated into a generic form until there has been enough mastery of the specifics of the situation to permit the discovery of lower order regularities which can then be recombined into higher-order, more generic coding systems. ”—Jerome Bruner, Going Beyond the Information Given (1973) 14 Worcester Polytechnic Institute

LEARNING • Thorndike, Woodworth, et al. were among the first to use transfer tests to examine assumptions about learning (1901) • Initial learning is necessary for transfer • Knowledge that is overly contextualized can reduce transfer • Transfer is an active, dynamic process All new learning involves transfer based on previous learning Mestre et al. , Rebello et al. , etc. Worcester Polytechnic Institute 15

FACTORS THAT INFLUENCE TRANSFER • Time on Task (e. g. Garner 1974) • Motivation to Learn (e. g. Schwartz et al. , 1999) • Context (e. g. Lave, 1988) • Problem Representations (e. g. Spiro et al. , 1991) • Relationship between Learning and Transfer Conditions (e. g. Brown 1986) 16 Worcester Polytechnic Institute

Assessment Tools in E&M • CSEM: Conceptual Survey in Electricity and Magnetism; Hieggelke, Maloney, O’Kuma, Van Heuvelen • DEEM: Diagnostic Exam in Electricity and Magnetism; Marx • DIRECT: Determining and Interpreting Resistive Electric Circuits Concepts Test ; Engelhardt and Beichner • BEMA: Brief Electricity and Magnetism Assessment; Ding, Chabay, Sherwood, Beichner Worcester Polytechnic Institute 17

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DEEM To fill the need for a tool testing introductory, undergraduates' knowledge of basic concepts in electricity and magnetism (EM), the investigator has developed a sixty-six item, multiple-choice diagnostic exam (DEEM). The exam is intended to provide physics instructors with a psychometrically sound instrument that serves three general purposes: (1) gauge students' pre-instructional knowledge (baseline assessment), assess students' postinstructional achievement, and provide scores to determine students' conceptual learning gains; (2) yield results that are maximally diagnostic to instructors by highlighting students' most common misconceptions and reveling patterns of responses which are easily interpreted by physics instructors; and (3) provide the physics education research community with a tool to measure the relative effectiveness of various curricula. The exam covers the following basic concepts of EM: forces on charged particles in electric or magnetic fields; properties of electric fields and magnetic fields; properties of electrostatic potential and potential energy; Maxwell's Equations; and induction, with Lenz's Law. Items comprising the DEEM do not require calculus, explicit calculations, or memorization of fundamental constants; are pictorially based; and generally explore highsymmetry scenarios. Reference: http: //www. compadre. org/per/items/detail. cfm? ID=3786 Worcester Polytechnic Institute 19

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BEMA Evaluating an electricity and magnetism assessment tool: Brief electricity and magnetism assessment written by Lin Ding, Ruth Chabay, Bruce Sherwood, and Robert J. Beichner The Brief Electricity and Magnetism Assessment (BEMA), developed by Chabay and Sherwood, was designed to assess student understanding of basic electricity and magnetism concepts covered in college-level calculus-based introductory physics courses. To evaluate the reliability and discriminatory power of this assessment tool, we performed statistical tests focusing both on item analyses (item difficulty index, item discrimination index, and item point biserial coefficient) and on the entire test (test reliability and Ferguson's delta). The results indicate that BEMA is a reliable assessment tool. Physical Review Special Topics - Physics Education Research: Volume 2, Issue 1, Pages 7 Reference: http: //prst-per. aps. org/abstract/PRSTPER/v 2/i 1/e 010105 Worcester Polytechnic Institute 21

Pilot Study at WPI (Spring 06) • Sophomore/Junior Level Course in Electricity and Magnetism at the level of Griffiths (N = 26: Frsh=4, Soph=18, Jr=2, Sr=2) • 85% class = PH majors; 15% = ECE majors • Female = 5 (19%), male = 21 (81%) 22 Worcester Polytechnic Institute

Course Background • Vector/Tensor Analysis is a prerequisite for the course • Material Discussed: Griffiths, Chapters 1, 2, 3, 5 • 2/3 of HW is traditional, 1/3 are visualizations in the Mastering. Physics framework (MP problems done in special classroom) Worcester Polytechnic Institute 23

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Hint for Question One 25 Worcester Polytechnic Institute

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Problem One (35 points): As shown in the diagram below, a rod of length L consists of a uniform line charge λ. (a) With V = 0 at infinity, what is V at P? (10 points) (b) On the diagram below, for the situation described in part (a), sketch the direction of the net electric field at point P (5 points). (c) Determine the electric potential, V, at point P, if the linear charge density is non-uniform and obeys the relationship λ = cx, where c is a constant having units of charge per length squared (15 points). (d) Set up, but do not evaluate, an expression for the electric field at Point P, for the situation described in part (c). (5 points) 35 Worcester Polytechnic Institute

Problem Three: Short Answer Questions: Please answer the following possibly unrelated questions, using a minimum of mathematics (5 points each, 30 points total). a. We give below three possible expressions for the z (vertical) component of the electric field at point P, Ez. Which one of these is correct? The circular loop has radius r and carries a uniform line charge λ. i. ) Ez = (2πr)(λ/(4πεo)) [z/(z 2 + r 2 )5/2 ] ii. ) Ez = (πr)(λ/(4πεo)) [1/(z 2 + r 2 ) ] iii. ) Ez = (2πr)(λ/(4πεo)) [z/(z 2 + r 2 )3/2 ] 36 Worcester Polytechnic Institute

Preliminary Data Average (%) Standard Deviation Mastering Physics Assignment 80 14 Traditional Homework Assignment 86 8 Exam Two 85 13 Exam Two, Question One 89 17 Exam Two, Question Three, Part A 99 0. 39 Student Ranked Degree of Helpfulness*** 2. 96 0. 87 37 Worcester Polytechnic Institute ***Likert Scale: 1 -5

Correlation Matrix**** (1) (2) (3) (4) (1) Mastering. Physics Assignment 1. 00 0. 41 0. 37 0. 26 (2) Traditional Homework Assignment 0. 41 1. 00 0. 21 0. 01 (3) Exam Two 0. 37 0. 21 1. 00 0. 81 (4) Exam Two, Question One 0. 26 0. 01 0. 81 1. 00 Variables 38 Worcester Polytechnic Institute ****Product Moment Correlation

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Student Feedback “The Java applets were moderately interesting, as were many of the visuals. However, many of the better ones were hidden in the hints, which the grade system encourages users to not view. ”—WPI Student “It was a good summary of the concepts we learned, but some of the visualizations were a little ambiguous. ”—Another WPI Student 42 Worcester Polytechnic Institute

FUTURE DIRECTIONS üMastering. Physics and Visualizations Pilot Study is currently ongoing at MIT. Findings? üRun more Comparison Tests: Academic Major, Gender, Class Year, CSEM gains üInterview students at both WPI and MIT to learn specific misconceptions and revise curricular materials as needed üShould the Mastering. Physics assignment be more difficult than the traditional homework assignment (addressing the context morphology issue)? 43 Worcester Polytechnic Institute

EPILOGUE “We talk about transfer of learning when learning is displayed in a situation somewhat different from that in which the original learning occurred. If the transfer situation is so different that the use of learning encounters some barrier or difficulty, we speak of problem solving. When the situation is greatly different and the distance of transfer needed is greater still, we speak of creativity. ”—Wilbert Mc. Keachie, Teaching and Learning in the College Classroom (1986). Worcester Polytechnic Institute 44